Graph fibrations, graph isomorphism, and pageRank

RAIRO - Theoretical Informatics and Applications

Volumn 40, Issue 2, 2006, Pages 227-253

  Boldi, Paolo ^a   Lonati, Violetta ^a   Santini, Massimo ^a   Vigna, Sebastiano ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

Graph fibrations; Markov chain with restart; PageRank

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; CONSTRAINT THEORY; FINITE DIFFERENCE METHOD; MARKOV PROCESSES; POLYNOMIALS;

GRAPH FIBRATIONS; MARKOV CHAIN WITH RESTART; PAGERANK;

GRAPH THEORY;

EID: 33746308367     PISSN: 09883754     EISSN: 28047346     Source Type: Journal    
DOI: 10.1051/ita:2006004     Document Type: Article

References (33)

1. P. Boldi, M. Santini and S. Vigna, PageRank as a function of the damping factor, in Proc. of the Fourteenth International World Wide Web Conference. ACM Press. Chiba, Japan (2005) 557-566.
2. P. Boldi and S. Vigna, Fibrations of graphs. Discrete Math. 243 (2002) 21-66.
3. P. Boldi and S. Vigna, The WebGraph framework I: Compression techniques, in Proc. of the Thirteenth International World Wide Web Conference. ACM Press, Manhattan, USA (2004) 595-601.
4. 2 |V|). Theoret. Comput. Sci. 19 (1982) 85-98.
5. D.G. Corneil and C.C. Gotlieb, An efficient algorithm for graph isomorphism. J. Assoc. Comput. Mach. 17 (1970) 51-64.
6. L. Eldén, The eigenvalues of the google matrix. Technical Report LiTH-MAT-R-04-01, Department of Mathematics, Linköping University, 2004. Available at http://arxiv.org/abs/math.RA/0401177.
7. G.H. Golub and C. Greif, Arnoldi-type algorithms for computing stationary distribution vectors, with application to PageRank, Technical Report SCCM-04-15, Stanford University Technical Report (2004).
8. M. Gori, M. Maggini and L. Sarti, Exact and approximate graph matching using random walks. IEEETPAMI: IEEE Trans. Pattern Anal. Machine Intelligence 27 (2005) 1100-1111.
9. J.L. Gross and T.W. Tucker, Topological Graph Theory, Series in Discrete Mathematics and Optimization, Wiley-Interscience (1987).
10. A. Grothendieck, Technique de descente et théorèmes d'existence en géométrie algébrique, I. Généralités. Descente par morphismes fidèlement plats. Seminaire Bourbaki 190 (1959-1960).
11. T.H. Haveliwala, Efficient computation of PageRank. Technical Report 31, Stanford University Technical Report, October 1999. Available at http://dbpubs.stanford.edu/pub/1999-31.
12. T.H. Haveliwala, Topic-sensitive pagerank, in The eleventh International Conference on World Wide Web Conference. ACM Press (2002) 517-526.
13. T.H. Haveliwala and S.D. Kamvar, The second eigenvalue of the Google matrix. Technical Report 80, Stanford University Technical Report, March 2003. Available at http://dbpubs.stanford.edu/pub/2003-20.
14. P. Híc, R. Nedela and S. Pavlíková, Front-divisors of trees. Acta Math. Univ. Comenian. (N.S.) 61 (1992) 69-84.
15. J.E. Hopcroft, An n log n algorithm for minimizing states in a finite automaton, in Theory of Machines and Computations, edited by Z. Kohavi and A. Paz. Academic Press (1971).
16. M. Iosifescu, Finite Markov Processes and Their Applications. John Wiley & Sons (1980).
17. S.D. Kamvar, T.H. Haveliwala, C.D. Manning and G.H. Golub, Exploiting the block structure of the web for computing PageRank. Technical Report 17, Stanford University Technical Report, March 2003. Available at http://dbpubs.stanford.edu/pub/2003-17.
18. S.D. Kamvar, T.H. Haveliwala, C.D. Manning and G.H. Golub, Extrapolation methods for accelerating PageRank computations, in Proceedings of the twelfth international conference on World Wide Web. ACM Press (2003) 261-270.
19. T. Kato, Perturbation Theory for Linear Operators. Springer-Verlag, second edition (1976).
20. L. László, Random walks on graphs: A survey, in Combinatorics, Paul Erdos is Eighty, Vol. 2, Bolyai Society Mathematical Studies, 1993, in Proceedings of the Meeting in honour of P. Erdos, Keszthely, Hungary 7 (1993) 1-46.
21. C. Pan-Chi Lee, G.H. Golub and S.A. Zenios, A fast two-stage algorithm for computing PageRank and its extensions. Technical Report SCCM-03-15, Stanford University Technical Report (2003). Available at http://www-sccm.stanford.edu/ pub/sccm/sccm03-15_2.pdf.
22. D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge UK (1995).
23. B.D. McKay, Practical graph isomorphism. Congressus Numerantium 30 (1981) 45-87.
24. C.D. Meyer, Matrix analysis and applied linear algebra. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2000).
25. M. Nasu, Constant-to-one and onto global maps of homomorphisms between strongly connect graphs. Ergod. Th. & Dynam. Sys. 3 (1983) 387-413.
26. N. Norris, Universal covers of graphs: Isomorphism to depth n - 1 implies isomorphism to all depths. Discrete Appl. Math. 56 (1995) 61-74.
27. L. Page, S. Brin, R. Motwani and T. Winograd, The PageRank citation ranking: Bringing order to the web. Technical Report 66, Stanford University, 1999. Available at http://dbpubs.stanford.edu/pub/1999-66.
28. D.M. Cvetković, M. Doob and H. Sachs, Spectra of Graphs. Academic Press (1978).
29. J.P. Schweitzer. Perturbation theory and finite markov chains. J. Appl. Probab. 5 (1968) 401-413.
30. E. Seneta, Non-negative matrices and Markov chains. Springer-Verlag, New York (1981).
31. S.H. Unger, GIT - A heuristic program for testing pairs of directed line graphs for isomorphism. Comm. ACM 7 (1964) 26-34.
32. S. Vigna, A guided tour in the topos of graphs. Technical Report 199-97, Università di Milano, Dipartimento di Scienze dell'Informazione, 1997. Available at http://vigna.dsi.unimi.it/ftp/papers/ToposGraphs.pdf.
33. K. Yosida, Functional Analysis. Springer-Verlag, (1980), Sixth Edition.